B Optimizing Stick Rotation in Space: Ideal Center of Mass Placement

  • Thread starter Thread starter Erunanethiel
  • Start date Start date
  • Tags Tags
    Space
Click For Summary
The discussion centers on the mechanics of a 10 cm stick in space and the optimal position of its center of mass (COM) for maximizing backward rotation when force is applied to one end. It is established that for a uniform stick, the COM is at the midpoint, and applying force at one end causes the stick to rotate around this point. The conversation explores how shifting the COM closer to the end where force is applied could enhance the backward motion of the opposite end, with participants considering various mass distributions. The importance of understanding torque and moment of inertia in relation to angular acceleration is emphasized, suggesting that concentrating mass at the COM can influence the stick's rotational response. Overall, the mechanics of rotation and the implications of mass distribution are key themes in the discussion.
  • #31
jbriggs444 said:
The original question is not well enough posed to have a definite answer. But yes, for a reasonable understanding of the intended question, the answer is "the middle".
PeroK put it way better than I did:When you give an impulse to one end of the rod, the COM moves forward and the object rotates around the COM. The initial velocity of the other end if the rod is the sum of the forward velocity of the COM and a backwards velocity from the rotation.

Question: what mass distribution will result in the other end of the rod initially moving backwards from its starting position with the greatest speed?
 
Physics news on Phys.org
  • #32
Erunanethiel said:
Question: what mass distribution will result in the other end of the rod initially moving backwards from its starting position with the greatest speed?
Answer: undefined. There is no optimum. The distribution with all of the mass exactly in the center results in an undefined speed and, accordingly, is ineligible.
 
  • #33
jbriggs444 said:
Answer: undefined. There is no optimum. The distribution with all of the mass exactly in the center results in an undefined speed and, accordingly, is ineligible.
Do you mean that the location of center of mass does not matter for this, the only thing that does is how "centralized" the mass is to CoM, irrespective of it's location. In short: Make every where that is not CoM make as light as possible.

Correct?
 
  • #34
Erunanethiel said:
Do you mean that the location of center of mass does not matter for this, the only thing that does is how "centralized" the mass is to CoM, irrespective of it's location. In short: Make every where that is not CoM make as light as possible.
The location of the center of mass relative to the ends matters. But so does the degree to which the mass is centralized. Both are relevant. One can even write an equation.

Try it. Apply an impulse "p" at right angles to one end of a rod of length "l" and mass "m" with center of mass offset "r" from the end where the impulse will be applied. If the rod has a moment of inertia "I", what speed will the other end have as a result?

Edit: Take it a step at a time. For instance, what rotation rate will result from the applied impulse?
 
  • #35
jbriggs444 said:
Answer: undefined. There is no optimum. The distribution with all of the mass exactly in the center results in an undefined speed and, accordingly, is ineligible.
Well, not that the other bits have no mass, they are as I said made as light as possible
 
  • #36
jbriggs444 said:
The location of the center of mass relative to the ends matters. But so does the degree to which the mass is centralized. Both are relevant. One can even write an equation.

Try it. Apply an impulse "p" at right angles to one end of a rod of length "l" and mass "m" with center of mass offset "r" from the end where the impulse will be applied. If the rod has a moment of inertia "I", what speed will the other end have as a result?

Edit: Take it a step at a time. For instance, what rotation rate will result from the applied impulse?
If the location of the center of mass relative to the ends matters, would the optimum position be in the middle, or closer to the side which the force is applied?
 
  • #37
Erunanethiel said:
If the location of the center of mass relative to the ends matters, would the optimum position be in the middle, or closer to the side which the force is applied?
Sorry, you are going to have to put some effort of your own into this problem. Until you do, I'm out.
 

Similar threads

Will a Stick in Space Rotate or Translate?
  • · Replies 1 ·
Replies
1
Views
2K
I How find moment of inertia for car in turn?
  • · Replies 49 ·
2
Replies
49
Views
5K
I Question about the velocity of the center of mass reference frame
  • · Replies 21 ·
Replies
21
Views
2K
B Strain on a foil sheet separating two compartments in a cylinder
  • · Replies 4 ·
Replies
4
Views
1K
Drumstick Rebound: Physics Behind Stick Stroke & Rotation Point
  • · Replies 5 ·
Replies
5
Views
7K
B Understanding air flow and resistance
  • · Replies 3 ·
Replies
3
Views
2K
B Determine forces acting on double inclined plane
  • · Replies 13 ·
Replies
13
Views
2K
I Measuring Spacing with Shortcut Technique: Is Uniformity Achieved?
  • · Replies 3 ·
Replies
3
Views
2K
B Lever balancing physics (video game design)
  • · Replies 18 ·
Replies
18
Views
2K
B Stability of Droplet Climbing on a Needle with Varying Contact Angle
  • · Replies 2 ·
Replies
2
Views
2K